A numerical investigation of the evaporation process of a liquid droplet impinging onto a hot substrate

A numerical investigation of the evaporation process of n-heptane and water liquid droplets impinging onto a hot substrate is presented. Three different temperatures are investigated, covering flow regimes below and above Leidenfrost temperature. The Navier–Stokes equations expressing the flow distribution of the liquid and gas phases, coupled with the Volume of Fluid Method (VOF) for tracking the liquid–gas interface, are solved numerically using the finite volume methodology. Both two-dimensional axisymmetric and fully three-dimensional domains are utilized. An evaporation model coupled with the VOF methodology predicts the vapor blanket height between the evaporating droplet and the substrate, for cases with substrate temperature above the Leidenfrost point, and the formation of vapor bubbles in the region of nucleate boiling regime. The results are compared with available experimental data indicating the outcome of the impingement and the droplet shape during the impingement process, while additional information for the droplet evaporation rate and the temperature and vapor concentration fields is provided by the computational model.     

Experimental and numerical investigation of droplet evaporation under diesel engine conditions

Evaporation of mono-disperse fuel droplets under high temperature and high pressure conditions is investigated. The time-dependent growth of the boundary layer of the droplets and the influence of neighboring droplets are examined analytically. A transient Nusselt number is calculated from numerical data and compared to the quasi-steady correlations available in literature. The analogy between heat and mass transfer is tested considering transient and quasi-steady calculations for the gas phase up to the critical point for a single droplet. The droplet evaporation in a droplet chain is examined numerically. Experimental investigations are performed to examine the influence of neighboring droplets on the drag coefficients. The results are compared with drag coefficient models for single droplets in a temperature range from T = 293–550 K and gas pressure p = 0.1–2 MPa. The experimental data provide basis for model validation in computational fluid dynamics.     

Advanced models of fuel droplet heating and evaporation

Recent developments in modelling the heating and evaporation of fuel droplets are reviewed, and unsolved problems are identified. It is noted that modelling transient droplet heating using steady-state correlations for the convective heat transfer coefficient can be misleading. At the initial stage of heating stationary droplets, the well known steady-state result Nu=2 leads to under prediction of the rate of heating, while at the final stage the same result leads to over prediction. The numerical analysis of droplet heating using the effective thermal conductivity model can be based on the analytical solution of the heat conduction equation inside the droplet. This approach was shown to have clear advantages compared with the approach based on the numerical solution of the same equation both from the point of view of accuracy and computer efficiency. When highly accurate calculations are not required, but CPU time economy is essential then the effect of finite thermal conductivity and re-circulation in droplets can be taken into account using the so called parabolic model. For practical applications in computation fluid dynamics (CFD) codes the simplified model for radiative heating, describing the average droplet absorption efficiency factor, appears to be the most useful both from the point of view of accuracy and CPU efficiency. Models describing the effects of multi-component droplets need to be considered when modelling realistic fuel droplet heating and evaporation. However, most of these models are still rather complicated, which limits their wide application in CFD codes. The Distillation Curve Model for multi-component droplets seems to be a reasonable compromise between accuracy and CPU efficiency. The systems of equations describing droplet heating and evaporation and autoignition of fuel vapour/air mixture in individual computational cells are stiff. Establishing hierarchy between these equations, and separate analysis of the equations for fast and slow variables may be a constructive way forward in analysing these systems.     

Mono-component fuel droplet evaporation in the presence of background fuel vapor

A simplified set of equations is examined for the problem of droplet evaporation. The equations employ the Clausius–Clapeyron (CC) boundary condition for the surface fuel-vapor, which is responsible for mathematical behaviors that include an initial condensation stage of droplet swelling followed by an evaporation stage. Numerical methods of analysis are used in conjunction with an asymptotic analysis of each of the three stages: (I) condensation; (II) transition; and (III) evaporation. Droplet evaporation in partial condensation environments is discussed.     

Radiation-enhanced evaporation of ethanol fuel containing suspended metal nanoparticles

Although the enhanced thermal conductivity of nanofluids has attracted much attention, their radiative properties have rarely been studied. The present paper quantitatively determined the radiative properties of various nanofluid fuels and their effects on droplet evaporation. The results show that radiation absorption can be significantly enhanced by adding a small amount of nanoparticles such as Al to the base fluid ethanol. The strong absorption of radiation energy by nanoparticles increases the nanofluid droplet temperatures and enhances droplet evaporation rate.     

Thermal droplet size measurements using a thermocouple

During the investigation on atomization and evaporation of water in steam spray coolers a thermal measuring device has been developed for droplet size measurement. This device consists of a thermocouple on which the droplet evaporates by heat removal from the thermocouple material near the hot junction; it is called: droplet detecting thermocouple (d.d.t.). The principle of a d.d.t. is based on utilization of the correlation between droplet radius and temperature signal of the d.d.t., caused by the evaporating droplet. The d.d.t. proved to be a dependable device for continuous detecting and measurement of water droplets both in air and steam flows, even at high pressures and temperatures. In this paper a theoretical analysis of the d.d.t. behaviour is given together with experimental data of d.d.ts. for water droplets with radii between 3 and 1188 μm. Good agreement between experimental data and theoretically predicted results has been reached.     

Three-dimensional numerical investigation on wall film formation and evaporation in port fuel injection engines

ABSTRACT

Wall film formation and evaporation were studied on a flat wall inside a constant-volume vessel using a three-dimensional numerical method. The computation was based on the discrete phase model (DPM) of spray dispersion, a spray–wall interaction model coupled with an enhanced wall film evaporation sub-model, in which the operating conditions of cold wall are considered for port fuel injection (PFI) engines. The influence of impacting parameters including injection pressure, the impingement distance from the injector and the impinged wall, injection duration, impingement angle, and wall temperature was discussed.     

Effects of gravity and ambient pressure on liquid fuel droplet evaporation

An axisymmetric numerical model has been developed to conduct a study of single droplet evaporation over a wide range of ambient pressures both under normal and microgravity conditions. Results for droplet lifetime as a function of ambient pressure and initial droplet diameter are presented. The enhancement in the droplet evaporation rate due to natural convection is predicted. This enhancement becomes more dominant with increasing ambient pressure due to the increase in the Grashof number. The higher the ambient pressure, the closer the Grashof number remains to its initial value throughout most of the droplet lifetime because of the droplet swelling and the heat-up of the droplet interior. Results should be particularly of interest to researchers conducting experiments on droplet evaporation at elevated pressures within a normal gravity environment. The model developed is in good agreement with experimental data at low pressures. Explanations have been provided for its deviation at high pressures.     

An experimental investigation of the breakup characteristics of secondary atomization of emulsified fuel droplet

In this study, the breakup characteristics of secondary atomization of an emulsified fuel droplet were investigated with a single droplet experiment. In the single droplet experiment, the emulsified fuel droplet suspended from a fine wire was inserted into an electric furnace, and then secondary atomization behavior was observed using a high-speed video camera. Moreover, a mathematical model to calculate the generated water vapor at micro-explosion was proposed by using the mass and energy conservation equations under some assumptions. In the proposed model, that can be calculated by using the inner droplet temperature history at micro-explosion. As a result, puffing and micro-explosion occurred even when the fine ceramics fiber was used. The proposed model showed that about 50–70 wt% of water in the emulsified fuel changed to water vapor instantaneously at the occurrence of micro-explosion. The mass of water necessary for micro-explosion was shown. The breakup time was closely related to the superheat temperature just before the occurrence of micro-explosion.     

Experimental and numerical analysis of the temperature transition of a suspended freezing water droplet

The objective of this study was to develop a simple experimental and numerical method to study the temperature transition of freezing droplets. One experimental approach and several numerical methods were explored. For the experimental method, a droplet was suspended in a cold air stream from the junction of a thermocouple. The droplet’s temperature transition was able to be accurately measured and the freezing of the droplet observed. The numerical models developed were able to predict the temperature transition and the freezing time of the droplet. Of the numerical methods, a simple heat balance model was determined to be an accurate means of predicting the freezing time of the droplet.     

New approaches to numerical modelling of droplet transient heating and evaporation

New approaches to numerical modelling of droplet heating and evaporation by convection and radiation from the surrounding hot gas are suggested. The finite thermal conductivity of droplets and recirculation in them are taken into account. These approaches are based on the incorporation of new analytical solutions of the heat conduction equation inside the droplets (constant or almost constant h) or replacement of the numerical solution of this equation by the numerical solution of the integral equation (arbitrary h). It is shown that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. This solution is applied to the first time step, using the initial distribution of temperature inside the droplet. The results of the analytical solution over this time step are used as the initial condition for the second time step etc. This approach is applied to the numerical modelling of fuel droplet heating and evaporation in conditions relevant to diesel engines, but without taking into account the effects of droplet break-up. It is shown to be more effective than the approach based on the numerical solution of the discretised heat conduction equation inside the droplet, and more accurate than the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating and evaporation allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.     

A molecular dynamics simulation investigation of fuel droplet in evolving ambient conditions

Molecular dynamics simulations are applied to model fuel droplet surrounded by air in a spatially and temporally evolving environment. A numerical procedure is developed to include chemical reactions into molecular dynamics. The model reaction is chosen to allow investigation of the position of chemical reactions (gas phase, surface, liquid phase) and the behavior of typical products (alcohols and aldehydes). A liquid droplet at molecular scale is seen as a network of fuel molecules interacting with oxygen, nitrogen, and products of chemical fuel breakdown. A molecule is evaporating when it loosens from the network and diffuses into the air. Naturally, fuel molecules from the gas phase, oxygen and nitrogen molecules can also be adsorbed in the reverse process into the liquid phase. Thus, in the presented simulations the time and length scales of transport processes – oxygen adsorption, diffusion, and fuel evaporation are directly determined by molecular level processes and not by model constants. In addition, using ab initio calculations it is proven that the reaction barriers in liquid and gas phases are similar.     

A numerical investigation on dynamics of ferrofluid droplet in nonuniform magnetic field

This article presents a 3D numerical investigation on ferrofluid droplet motion in magnetic field using VOSET. A nonuniform magnetic field mimicking the one produced by an electric wire loop was generated in a finite computational domain. A validation problem on droplet deformation in uniform magnetic field was first studied, and it gives consistent aspect ratios with reported experiments. The simulation revealed an entire process of the ferrofluid droplet movement, and the influences by the intensity of the magnetic field was investigated and analyzed. Finally, a set of simulations were conducted for net magnetic force on spherical droplet, and the achieved data led to a correlation, which gives accurate prediction in the magnitude of the magnetic force and can be applied to droplet with a certain degree of deformation.     

A molecular dynamics simulation of droplet evaporation

A molecular dynamics (MD) simulation method is developed to study the evaporation of submicron droplets in a gaseous surrounding. A new methodology is proposed to specify initial conditions for the droplet and the ambient fluid, and to identify droplet shape during the vaporization process. The vaporization of xenon droplets in nitrogen ambient under subcritical and supercritical conditions is examined. Both spherical and non-spherical droplets are considered. The MD simulations are shown to be independent of the droplet and system sizes considered, although the observed vaporization behavior exhibits some scatter, as expected. The MD results are used to examine the effects of ambient and droplet properties on the vaporization characteristics of submicron droplets. For subcritical conditions, it is shown that a spherical droplet maintains its sphericity, while an initially non-spherical droplet attains the spherical shape very early in its lifetime, i.e., within 10% of the lifetime. For both spherical and non-spherical droplets, the subcritical vaporization, which is characterized by the migration of xenon particles that constitute the droplet to the ambient, exhibits characteristics that are analogous to those reported for “continuum-size” droplets. The vaporization process consists of an initial liquid-heating stage during which the vaporization rate is relatively low, followed by nearly constant liquid-temperature evaporation at a “pseudo wet-bulb temperature”. The rate of vaporization increases as the ambient temperature and/or the initial droplet temperature are increased. For the supercritical case, the droplet does not return to the spherical configuration, i.e., its sphericity deteriorates sharply, and its temperature increases continuously during the “vaporization” process.     

A numerical study of the effect of turbulence on mass transfer from a single fuel droplet evaporating in a hot convective flow

A three-dimensional numerical model is developed to investigate the effect of turbulence on mass transfer from a single droplet exposed to a freestream of air. The freestream temperature, turbulence intensity and Reynolds number are varied to provide a wide range of test conditions, whereas the ambient pressure is kept atmospheric. The turbulence terms in the conservation equations of the gas-phase are modelled by using the shear-stress transport (SST) model. A Cartesian grid based blocked-off technique is used in conjunction with the finite-volume method to solve numerically the governing equations of the gas and liquid-phases. This study showed that the vaporization Damköhler number proposed in the literature to correlate the effect of turbulence on the droplet's vaporization rate is invalid at air temperatures higher than room temperature. Additionally, an attempt is made to correlate the effect of the freestream turbulence on the droplet's mass transfer rate by using Sherwood number over a wide range of freestream temperatures.     

Two-phase modeling of evaporation characteristics of ethanol droplet under force-convection environment

Studies on the evaporation phenomenon of a pure ethanol droplet have been mostly confined to the semianalytical modeling in stagnant ambient. Investigation into this aspect in a convective environment by considering the Navier–Stokes equation is also minimal. Hence, in this study we analyze and investigate the evaporation characteristics of a single-component spherical-shaped isolated pure ethanol droplet under force convective air environment by considering both gas- and liquid-phase motions, nonunitary Lewis number in the interface, variable Stefan flow (blowing) effect, and the transient droplet heating. The finite difference method is utilized while solving the governing equations of the spherical polar coordinate system for species, momentum, and energy transfer. The maximum Reynolds number and ambient temperature are kept at 100 and 600 K, respectively. The present work is validated by comparing the normalized surface regression curve of the droplet with the earlier experimental and theoretical results. Using the current simulated data, flow and temperature profiles of both gas and liquid regions are visualized in streamline and isotherm contour plots at various instants of time. It is observed that at a moderate Reynolds number a detached vortex forms at the downstream location of the droplet. However, the detachment length increases with time. The temperature gradients along the droplet surface are observed at the initial stage. Moreover, the heat-up period occupies about 20% of the total lifetime of the droplet. The droplet life and heat-up period decrease with an increase in free-stream velocity. In addition, the saturation temperature increases with ambient temperature.     

Finite-rate evaporation and droplet drag effects in spherical flame front propagation through a liquid fuel mist

An evolution equation for a laminar flame front propagating into an air and liquid fuel mist cloud is derived for the first time, accounting for both the finite-rate evaporation of the fuel droplets and the slip velocity between them and their host environment. The asymptotic analysis employed in developing the equation exploits the usual inverse large activation energy parameter associated with chemical reaction in the flame and a small drag parameter. It is demonstrated that, in the no-slip velocity case, increasing the vaporization Damköhler number can produce flame extinction, presumably due to the more intense heat loss incurred due to droplet heat absorption necessary for vaporization. Droplet drag can also induce extinction due to the longer residence time of the droplets in any locale (than if there was no slip), leading to more vaporization with greater attendant heat loss. The predicted results for droplet velocity are compared to independent experimental data from the literature with good qualitative agreement.     

A model for droplet evaporation near Leidenfrost point

The droplet evaporation process after impinging on a solid wall near Leidenfrost point is theoretically analyzed. Considering the change of heat transfer effective in the evaporation process, it is divided into recoil stage and spherical stage, and the heat transfer models in these two stages are built, respectively. The effect of initial Weber number, initial droplet diameter, solid surface superheat and wettbility are included in the models. A correlation for predicting evaporation lifetime is obtained based on the theoretical analysis and experimental results. By comparing analysis results with experimental data, it is concluded that the evaporation process can be predicted by present model. The results imply that Leidenfrost point may be not the turning point of heat transfer mechanism. The effect of drop size and Weber number are also analyzed.     

Thermal characteristics of an air-cooled open-cathode proton exchange membrane fuel cell stack via numerical investigation

In light of stricter emissions regulations and depleting fossil fuel reserves, fuel cell vehicles (FCVs) are one of the leading alternatives for powering future vehicles. An open-cathode, air-cooled proton exchange membrane fuel cell (PEMFC) stack provides a relatively simple electric generation system for a vehicle in terms of system complexity and number of components. The temperature within a PEMFC stack is critical to its level of performance and the electrochemical efficiency. Previously created computational models to study and predict the stack temperature have been limited in their scale and the inaccurate assumption that temperature is uniform throughout. The present work details the creation of a numerical model to study the temperature distribution of an 80-cell Ballard 1020ACS stack by simulating the cooling airflow across the stack. Using computational fluid dynamics, a steady-state airflow simulation was performed using experimental data to form boundary conditions where possible. Additionally, a parametric study was performed to investigate the effect of the distance between the stack and cooling fan on stack performance. Model validation was performed against published results. The temperature distribution across the stack was identical for the central 70% of the cells, with eccentric temperatures observed at the stack extremities, while the difference between coolant and bipolar plate temperatures was approximately 10°C at the cooling channel outlets. The results of the parametric study showed that the fan-stack distance has a negligible effect on stack performance. The assumptions regarding stack temperature uniformity and measurement were challenged. Lastly, the hypothesis regarding the negligible effect of fan-stack distance on stack performance was confirmed.     

A numerical investigation on multi-phase transport phenomena in a proton exchange membrane fuel cell stack

In this study, the simulation of a fuel cell stack is performed by applying a general numerical model with VOF method that has been successfully applied to single PEMFC model to investigate the fluid dynamics, mass transport, flooding phenomenon and the effects of liquid water on the stack performance. The performance of three single cells in series connection in the fuel cell stack is examined according to the presence of liquid water in different single cells. The distributions of fluid flow, species concentration and the current density are presented to illustrate the effects of liquid water on the performance of each single cell. The numerical results locate that the low distributions of species in the flooding cell certainly degrade the performance of this cell. Moreover, it can be seen that the performance of the flooding cell will significantly affect the whole stack performance since the values of average current density must be identical in all single cells.